Optimal sparse boundary control for a semilinear parabolic equation with mixed control-state constraints

• Autorzy: Casas Eduardo , Troltzsch Fredi
• Języki publikacji: EN

Abstrakty

EN

A problem of sparse optimal boundary control for a semilinear parabolic partial differential equation is considered, where pointwise bounds on the control and mixed pointwise control-state constraints are given. A standard quadratic objective functional is to be minimized that includes a Tikhonov regularization term and the L1-norm of the control accounting for the sparsity. Applying a recent linearization theorem, we derive first-order necessary optimality conditions in terms of a variational inequality under linearized mixed control state constraints. Based on this preliminary result, a Lagrange multiplier rule with bounded and measurable multipliers is derived and sparsity results on the optimal control are demonstrated.

Słowa kluczowe

EN

semilinear parabolic equation; optimal control; sparse boundary control; mixed control-state constraints

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2019
• Tom: Vol. 48, No. 1
• Strony: 89--124
• Opis fizyczny: Bibliogr. 19 poz., rys.

Twórcy

autor

Casas Eduardo

• Departamento de Matem´atica Aplicada y Ciencias de la Computaci´on, E.T.S.I. Industriales y de Telecomunicacion, Universidad de Cantabria, 39005 Santander, Spain

autor

Troltzsch Fredi

• Institut fur Mathematik, Technische Universitat Berlin, D-10623 Berlin, Germany

Bibliografia

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• [4] Casas, E. and Tr¨oltzsch, F. (2018b) State-constrained semilinear elliptic optimization problems with unrestricted sparse controls. To appear in Math. Control Rel. Fields.
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• [18] Rosch, A. and Tr¨oltzsch, F. (2007) On regularity of solutions and Lagrange multipliers of optimal control problems for semilinear equations with mixed pointwise control-state constraints. SIAM J. Control and Optimization, 46 (3), 1098–1115.
• [19] Temam, R. (1979) Navier-Stokes Equations. North-Holland, Amsterdam. Tr¨oltzsch, F. (1979) A minimum principle and a generalized bang-bang principle for a distributed optimal control problem with constraints on control and state. Z. Angew. Math. Mech., 59 (12), 737–739.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020)